One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

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Constraints

• 1 ≦ N ≦ 200,000
• (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3
2 1 3

Output

9

Input

4
1 3 2 4

Output

19

Input

8
5 4 8 1 2 6 7 3

Output

85

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